The Internet motivated video streaming systems are largely complicated by issues such as a high degree of network resource sharing amongst many flows, which potentially leads to deadlocks. Using concepts of siphons along with their corresponding dangerous markings, we derive an algebraically necessary and sufficient characterization for such a much undesirable situation. The target system is assumed to be described in a Petri net formalism, whose markings provide the information on the current interactions among related network operations and resources. The theoretic materials allow us to introduce the control laws iteratively. At each iteration step, we produce a generalized mutual exclusion constraint which contains only markings for which liveness can be enforced. Since the explicit enumeration of all siphons is avoided, the proposed method can greatly reduce the complexity of off-line computation for the on-line restriction policy. Furthermore, a generalized elementary siphon control investigation is involved such that the final supervisor can be structurally simplified. Examples are demonstrated in this paper to validate the effectiveness and efficiency of the proposed approach.

This paper presents a deadlock prevention algorithm for the class of sequential resource allocation system for flexible manufacturing systems, which allows for multiple resources flexible routings. Two classes of Petri nets Extended from Systems of Simple Sequential Processes with Resources (ES 3 PR) and Systems of Simple Sequential Processes with General Resource Requirements (S 3 PGR 2) whose deadlocks are related to unmarked siphons are considered. Based on the definition of ES 3 PR net, the original net is an ordinary Petri net. We further present a siphon-based algorithm of deadlock prevention for both classes of Petri nets. The proposed method is an iterative approach. We note that S 3 PGR 2 net structure is a weighted generalization of the ES 3 PR net. Based on this reason, the proposed algorithm can be applied to S 3 PGR 2 net if the target net is normalized to ordinary one. And this algorithm is only adding generalized control place. Finally, numerical experiments using reachability tree illustrate that the proposed algorithm appears to generate more permissive supervisors than the closely related approaches of other literatures.

Abstract—The RESTART method is an efficient algorithm to estimate low probabilities by simulation. It forces a rare event to be visited more frequently by splitting promising paths at certain thresholds. The achievable speedup depends heavily on the quality of the importance function, which controls the splitting behavior. It is well-known from the literature that the specification of a good importance function is a subtle task for non-trivial systems. In this paper we present ideas that have the potential to support finding an importance function for models expressed as a stochastic Petri net. It is shown how the frequency of a rare event of interest can be estimated a-priori to set the number of thresholds close to its optimal value. A measure for the distance between a current marking and the rare state is given as well. Both contributions rely on an algebraic formulation of the Petri net structure and use results for their further analysis as a linear programming problem. I.